Survivor question is a tricky one you know... Cat Burglar would technically win since he would probably just pick a lock and get the fuck out since non of the other ones are rich losers worth stealing from. But then is he "in-room-survivor"? Not really! Out!
BCD Neul has life experience but this baby tired of peoples bullshit. Or his own. Just in different AUs. He would probably pick a corner to take a nap. Out!
Size Queen Neul doesn't even really want a fight, baby you seen the prices on manicures these days? Cannot get those beautiful hands get damaged in any way! Out!
There we come to Haomega which would clearly win with one skill and one skill only - bullshitting. It is clearly established that the guy is an expert at going through life with fake-it-til-you-make-it attitude (and lots of hard work duh). He would 100% talk himself out of the situation, making him a clear survivor! Ding ding ding we have a winner!

As a bonus shower thought, I think if all the feelsofine Bins would be locked in a room, they would have a nice long talk, nice long cry and fully agree to go to group therapy :)

Sending all the energy you might need for writing <3!